E. Serra et al., ON THE EXISTENCE OF HOMOCLINIC SOLUTIONS FOR ALMOST-PERIODIC 2ND-ORDER SYSTEMS, Annales de l Institut Henri Poincare. Analyse non lineaire, 13(6), 1996, pp. 783-812
In this paper we prove the existence of at least one homoclinic soluti
on for a second order Lagrangian system, where the potential is an alm
ost periodic function of time. This result generalizes existence theor
ems known to hold when the dependence on time of the potential is peri
odic. The method is of a variational nature, solutions being found as
critical points of a suitable functional. The absence of a group of sy
mmetries for which the functional is invariant (as in the case of peri
odic potentials) is replaced by the study of problems ''at infinity''
and a suitable use of a property introduced by E. Sere.